A377375 Antidiagonal sums of A342819.

0, 0, 0, 4, 11, 25, 42, 70, 101, 147, 196, 264, 335, 429, 526, 650, 777, 935, 1096, 1292, 1491, 1729, 1970, 2254, 2541, 2875, 3212, 3600, 3991, 4437, 4886, 5394, 5905, 6479, 7056, 7700, 8347, 9065, 9786, 10582, 11381, 12259, 13140, 14104, 15071, 16125, 17182, 18330, 19481, 20727

Offset: 0

Author

Stefano Spezia, Dec 28 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Cf. A342819.

Programs

Mathematica

LinearRecurrence[{2,1,-4,1,2,-1},{0,0,0,4,11,25,42,70},50]

Formula

a(n) = (n - 2)*(2*n^2 + 10*n - 3*(1 + (-1)^n))/12 for n > 1.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n > 7.

G.f.: x^3*(4 + 3*x - x^2 - 3*x^3 + x^4)/((1 - x)^4*(1 + x)^2).

E.g.f.: (1 - x + x^2 + x^3/6)*cosh(x) - x*(9 - 6*x - x^2)*sinh(x)/6 - 1 + x.